x^3+8x^2+15x-1800=0

asked by guest
on Nov 13, 2024 at 1:37 am



You asked:

Solve the equation \({x}^{3} + 8 \cdot {x}^{2} + 15 x - 1800 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{8}{3} + \sqrt[3]{\frac{24328}{27} + \frac{5 \sqrt{292269}}{3}} + \frac{19}{9 \sqrt[3]{\frac{24328}{27} + \frac{5 \sqrt{292269}}{3}}} \approx 9.6758778\\x &= - \frac{\sqrt[3]{\frac{5 \sqrt{292269}}{3} + \frac{24328}{27}}}{2} - \frac{8}{3} - \frac{19}{18 \sqrt[3]{\frac{5 \sqrt{292269}}{3} + \frac{24328}{27}}} + i \left(- \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{5 \sqrt{292269}}{3} + \frac{24328}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5 \sqrt{292269}}{3} + \frac{24328}{27}}}{2}\right) \approx -8.8379389 + 10.388478 i\\x &= - \frac{\sqrt[3]{\frac{5 \sqrt{292269}}{3} + \frac{24328}{27}}}{2} - \frac{8}{3} - \frac{19}{18 \sqrt[3]{\frac{5 \sqrt{292269}}{3} + \frac{24328}{27}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5 \sqrt{292269}}{3} + \frac{24328}{27}}}{2} + \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{5 \sqrt{292269}}{3} + \frac{24328}{27}}}\right) \approx -8.8379389 -10.388478 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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